Although the on-board superconducting magnets (SCMs) ate a relatively small fraction of the cost and weight of Maglev systems their performance is critical to the success of the entire system. If the SCMs fail, even temporarily (via a quench), the vehicle will not levitate and backup propulsion must be employed. A very low velocity results and all of the vehicles in the system throughout the region may be affected. The velocity of the MLU002 in Japan had been limited by quenching of the SCMs due to track induced vibrations at high speed. In this paper, superconductor stability is discussed assuming time-dependent, spatially varying heat loads. The one-dimensional minimum-propagating zone (MPZ) model has been extended to include time-dependent disturbances. The MPZ has been determined as a function of the disturbance frequency, amplitude, and length. The spatial variation of the initial disturbance has been modeled as a sinusoidal function. Results for the MLU002 and cable-in-conduit-conductors are compared.